Solve graphically the following game:
$\begin{array}{ccc} &&B1&B2 \end{array} \\ \begin{array}{c} A1\\ A2\\ A3 \end{array} \left[ \begin{array} {cc} 3&-2 \\ -1&4 \\ 2 &2 \end{array} \right ]$
I have solved the question graphically and got two intersection points. The reduced matrix for both points are:
$\begin{array}{ccc} &&B1&B2 \end{array} \\ \begin{array}{c} A2\\ A3 \end{array} \left[ \begin{array}{cc} -1&4 \\ 2&2 \end{array} \right]$
and
$ \begin{array}{ccc} &&B1&B2 \end{array} \\ \begin{array}{c} A1\\ A3 \end{array} \left[ \begin{array}{cc} 3&-2 \\ 2&2 \end{array} \right]$
By using the probabilistic approach I got the value of the game to be 2 for both and strategy of A to be (0,0,1) for both points and strategy of B to be ($\frac{2}{5},\frac{3}{5}$) and ($\frac{4}{5},\frac{1}{5}$) respectively for the two points.
Later I realised both the reduced matrix have a saddle point. The value of game for both turn out to be 2 and best strategies for each point to be A3,B1 and A3,B2 respectively for each point.
Now I am confused which approach is correct. Can someone help me with this?